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Q)

Find all pairs of consecutive odd positive integers both of which all larg

Find all pairs of consecutive odd positive integers both of which all larger than 8 ,such that their sum is less than 34

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A)
Let x and x+2 be two consecutive even positive integers.

Since both the integer are larger then 8. x>8 -----(1)

Also sum of two is less than 34

x+x+2<34

=>2x+2<34

Adding -2 to both sides

2x<34−2

2x<32

Diving by 2 on both sides,

2x/2<16

x<16…………………..2

Since x is an even positive integer greater than 8 and less then 16 x can take value  8,10, 12,14 Thus the required pair of numbers is (8,10), (10,12),(12,14),(14,16)
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